CN102521439B - Calculation method of heat transfer coefficient of quenching medium combined with finite element method and inverse heat transfer method - Google Patents

Calculation method of heat transfer coefficient of quenching medium combined with finite element method and inverse heat transfer method Download PDF

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CN102521439B
CN102521439B CN201110395888.XA CN201110395888A CN102521439B CN 102521439 B CN102521439 B CN 102521439B CN 201110395888 A CN201110395888 A CN 201110395888A CN 102521439 B CN102521439 B CN 102521439B
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probe body
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朱景川
杨夏炜
来忠红
何东
刘勇
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Harbin Institute of Technology Shenzhen
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Abstract

The invention discloses a method for calculating a quenching medium heat exchange coefficient by combining a finite element method with an inverse heat conduction method, which relates to a method for calculating a quenching medium heat exchange coefficient. The method comprises the following steps of: using a probe body, testing by an experiment to obtain the cooling curve of an internal point of the body, establishing a finite element model of the probe body, simulating a temperature field, and verifying the one-dimensional property of a problem; establishing a one-dimensional heat conduction micro equation and a sensitive coefficient equation under a coordinate system, and solving the heat-flow density value of the surface of the body surface by using the inverse heat conduction method; and verifying the measured temperature of the internal point of the probe in comparison to a calculated value, namely the heat exchange coefficient of the quenching medium calculated according to the Newton heat exchange law, so that the solution accuracy is ensured. The method is used for calculating the heat exchange coefficient of quenching medium.

Description

结合有限元法和反传热法计算淬火介质换热系数的方法Calculation method of heat transfer coefficient of quenching medium combined with finite element method and inverse heat transfer method

技术领域 technical field

本发明涉及一种计算淬火介质换热系数的方法，属于金属热加工工艺参数设计领域。The invention relates to a method for calculating the heat transfer coefficient of a quenching medium, which belongs to the field of technical parameter design of metal thermal processing.

背景技术 Background technique

淬火处理在实际生产中是零件的一种非常重要的热处理方式，以获得需要的力学性能，而淬火介质无疑是最重要的影响因素，淬火介质的本质作用的体现是在其与金属表面之间的换热系数的大小。寻求精确的方法获取换热系数的大小具有重要的工程实际意义。目前，研究该问题的主要方法是反传热计算法，这种方法是一种理论的数学离散的计算方法，具有一定的不可避免的误差，导致无法精确控制工业零件的淬火冷却速度，冷却速度难以测量。Quenching treatment is a very important heat treatment method for parts in actual production to obtain the required mechanical properties, and the quenching medium is undoubtedly the most important influencing factor. The essential role of the quenching medium is reflected between it and the metal surface. The size of the heat transfer coefficient. Seeking an accurate method to obtain the size of the heat transfer coefficient has important engineering practical significance. At present, the main method to study this problem is the inverse heat transfer calculation method. This method is a theoretical mathematical discrete calculation method with certain inevitable errors, which makes it impossible to accurately control the quenching cooling rate of industrial parts. Difficult to measure.

发明内容 Contents of the invention

本发明的目的是为了解决通过反传热计算法获取换热系数的方法具有误差，导致无法精确控制工业零件的淬火冷却速度，冷却速度难以测量的问题，进而提供一种结合有限元法和反传热法计算淬火介质换热系数的方法。The purpose of the present invention is to solve the problem that the method of obtaining the heat transfer coefficient through the inverse heat transfer calculation method has errors, which leads to the inability to accurately control the quenching cooling rate of industrial parts, and the problem that the cooling rate is difficult to measure, and then provides a combination of finite element method and inverse The method of calculating the heat transfer coefficient of the quenching medium by the heat transfer method.

本发明是通过下述方案予以实现的：结合有限元法和反传热法计算淬火介质换热系数的方法，所述计算淬火介质换热系数的方法的具体过程为：The present invention is achieved through the following scheme: combining the finite element method and the reverse heat transfer method to calculate the heat transfer coefficient of the quenching medium, the specific process of the method for calculating the heat transfer coefficient of the quenching medium is as follows:

步骤一、将内部插有热电偶的探头本体在加热炉中加热到860℃保温均匀后，以不超过2s的转移时间迅速淬入淬火介质中，淬火介质温度设定为Tw，采用电脑系统记录由热电偶测得的探头本体内部特征点B3的温度，并绘制冷却曲线，即得到此温度下该淬火介质的冷却曲线；Step 1. Heat the probe body with the thermocouple inserted inside to 860°C in the heating furnace, and then quickly quench it into the quenching medium with a transfer time of no more than 2s. The temperature of the quenching medium is set to Tw , and the computer system is used. Record the temperature of the characteristic point B3 inside the probe body measured by the thermocouple, and draw the cooling curve, that is, the cooling curve of the quenching medium at this temperature is obtained;

步骤二、基于ABAQUS有限元平台，采用有限元的方法建立探头本体的有限元对称模型，输入探头本体材料的物理性能参数和力学性能参数，设定初始温度850℃，设定淬火介质温度Tw，选取换热系数极大值，选取一维模型的表面特征点A1和内部特征点B1，选取三维模型的表面特征点A2和内部特征点B2，一维模型的表面特征点A1与三维模型的表面特征点A2为同一位置点，一维模型内部特征点B1、三维模型内部特征点B2和探头本体内部特征点B3为同一点，然后分别采用一维模型和三维模型进行模拟计算并进行比较，探头本体在一维模型条件下表面特征点A1和三维模型条件下表面特征点A2的冷却曲线重合，探头本体在一维模型条件内部特征点B1和三维模型条件内部特征点B2的冷却曲线重合，验证换热问题符合的一维性质；Step 2. Based on the ABAQUS finite element platform, use the finite element method to establish a finite element symmetric model of the probe body, input the physical and mechanical performance parameters of the probe body material, set the initial temperature to 850°C, and set the quenching medium temperature T w , select the maximum heat transfer coefficient, select the surface feature point A1 and internal feature point B1 of the one-dimensional model, select the surface feature point A2 and internal feature point B2 of the three-dimensional model, and the surface feature point A1 of the one-dimensional model and the three-dimensional model The surface feature point A2 is the same position point, the internal feature point B1 of the one-dimensional model, the internal feature point B2 of the three-dimensional model and the internal feature point B3 of the probe body are the same point, and then the one-dimensional model and the three-dimensional model are used for simulation calculation and comparison. The cooling curves of the surface feature point A1 of the probe body under the one-dimensional model condition and the surface feature point A2 under the three-dimensional model condition coincide, and the cooling curves of the internal feature point B1 of the probe body under the one-dimensional model condition and the internal feature point B2 under the three-dimensional model condition coincide, Verify that the heat transfer problem conforms to the one-dimensional nature;

步骤三、根据能量守恒定律和傅里叶定律，建立圆柱坐标系下的一维导热微分方程，给出方程的初始条件和边界条件，并且定义与温度具有相同形式的敏感系数方程，给出敏感系数方程的初始条件和边界条件，利用反传热法求解探头本体表面的热流密度值；Step 3. According to the law of energy conservation and Fourier's law, establish a one-dimensional heat conduction differential equation in the cylindrical coordinate system, give the initial conditions and boundary conditions of the equation, and define the sensitivity coefficient equation with the same form as the temperature, and give the sensitivity The initial conditions and boundary conditions of the coefficient equation, using the inverse heat transfer method to solve the heat flux value on the surface of the probe body;

圆柱坐标系下的一维导热微分方程为：The one-dimensional heat conduction differential equation in the cylindrical coordinate system is:

ρcρc ∂∂ TT ∂∂ tt == 11 rr ∂∂ ∂∂ rr (( λrλr ∂∂ TT ∂∂ rr )) -- -- -- (( 11 ))

式中ρ为密度；c为比热容；T为探头本体表面温度；t为时间；λ为热传导系数；r为探头本体的半径；In the formula, ρ is the density; c is the specific heat capacity; T is the surface temperature of the probe body; t is the time; λ is the thermal conductivity; r is the radius of the probe body;

初始条件为：The initial conditions are:

T(r，tM-1)＝TM-1(r)                                 (2)T(r, t M-1 ) = T M-1 (r) (2)

式中tM-1为M-1时刻；TM-1(r)为tM-1时刻的温度分布；In the formula, t M-1 is the time of M-1; T M-1 (r) is the temperature distribution at the time of t M-1 ;

边界条件为：The boundary conditions are:

-- &lambda;&lambda; &PartialD;&PartialD; TT &PartialD;&PartialD; rr || rr == RR == qq Mm == constconst tt Mm -- 11 << tt << tt Mm qq (( tt )) tt >> tt Mm -- -- -- (( 33 ))

-- &lambda;&lambda; &PartialD;&PartialD; TT &PartialD;&PartialD; rr || rr == 00 == 00 -- -- -- (( 44 ))

式中R为探头本体的实际半径值；式中tM为M时刻；热流密度qM为常数；q(t)为t时刻的热流密度值；In the formula, R is the actual radius value of the probe body; in the formula, t M is the time M; the heat flux q M is a constant; q(t) is the heat flux value at the time t;

定义敏感系数为探头本体内部点温度测量误差的敏感程度，是温度关于热流密度的一级微商；The sensitivity coefficient is defined as the sensitivity of the temperature measurement error of the internal point of the probe body, which is the first-order derivative of the temperature with respect to the heat flux;

敏感系数表达式为：The expression of the sensitivity coefficient is:

&rho;c&rho;c &PartialD;&PartialD; Xx Mm &PartialD;&PartialD; tt == 11 rr &PartialD;&PartialD; &PartialD;&PartialD; rr (( &lambda;r&lambda;r &PartialD;&PartialD; Xx Mm &PartialD;&PartialD; rr )) -- -- -- (( 55 ))

式中XM为敏感系数；Where X M is the sensitivity coefficient;

初始条件为：The initial conditions are:

XM(r，tM-1)＝0                                      (6)X M (r, t M-1 ) = 0 (6)

式中XM为敏感系数；Where X M is the sensitivity coefficient;

边界条件为：The boundary conditions are:

-- &lambda;&lambda; &PartialD;&PartialD; Xx Mm &PartialD;&PartialD; rr || rr == RR == 11 tt Mm -- 11 << tt << tt Mm 00 tt >> tt Mm -- -- -- (( 77 ))

-- &lambda;&lambda; &PartialD;&PartialD; TT &PartialD;&PartialD; rr || rr == 00 == 00 -- -- -- (( 88 ))

敏感系数对热流密度值进行修正，利用反传热法求解M时刻的热流密度值，反复计算得整个淬火过程的热流密度值q；The sensitivity coefficient corrects the heat flux value, uses the inverse heat transfer method to solve the heat flux value at M time, and repeatedly calculates the heat flux value q of the entire quenching process;

步骤四、根据牛顿换热定律来计算金属与介质表面的换热系数，即得到了介质的换热系数；牛顿换热定律表达式为：Step 4. Calculate the heat transfer coefficient between the metal and the surface of the medium according to Newton's law of heat transfer, that is, the heat transfer coefficient of the medium is obtained; the expression of Newton's law of heat transfer is:

q＝h(T-Tw)                                                (9)q=h(TT w ) (9)

式中q为热流密度值，h为换热系数，(T-Tw)为探头表面温度与设定介质温度的差值；In the formula, q is the heat flux value, h is the heat transfer coefficient, (TT w ) is the difference between the probe surface temperature and the set medium temperature;

本技术方案中将步骤一中热电偶测得的探头本体内部特征点B3的温度，并绘制的冷却曲线与步骤二中探头本体在三维模型条件内部特征点B2的冷却曲线进行对比，两者吻合，验证了换热系数求解的精确性。In this technical solution, the temperature of the internal characteristic point B3 of the probe body measured by the thermocouple in step 1, and the drawn cooling curve are compared with the cooling curve of the internal characteristic point B2 of the probe body in the three-dimensional model condition in step 2, and the two coincide. , which verifies the accuracy of the heat transfer coefficient solution.

本发明的有益效果：本发明提出了结合有限元法和反传热法计算淬火介质换热系数的方法，基于成熟的ABAQUS有限元软件，保证了计算结果的可信度和准确性，在此基础上结合传统的反传热法以更准确和更可靠的方法去求解淬火介质的换热系数。该方法的提出，精确的控制了工业零件的淬火冷却速度，避免冷却速度难于测量的问题，并将该方法进行推广，通过测试不同介质的冷却曲线求得其与金属表面的换热系数，然后设计淬火介质，使零件在工业中获得满意的力学性能，适应各种环境下，服役的性能需求。Beneficial effects of the present invention: the present invention proposes the method combining finite element method and inverse heat transfer method to calculate the heat transfer coefficient of quenching medium, based on the mature ABAQUS finite element software, to ensure the credibility and accuracy of the calculation results, here Based on the traditional inverse heat transfer method, a more accurate and reliable method is used to solve the heat transfer coefficient of the quenching medium. The proposal of this method accurately controls the quenching cooling rate of industrial parts, avoids the problem that the cooling rate is difficult to measure, and promotes this method, and obtains the heat transfer coefficient between it and the metal surface by testing the cooling curves of different media, and then Design the quenching medium to make the parts obtain satisfactory mechanical properties in the industry, and adapt to the performance requirements of service in various environments.

附图说明 Description of drawings

图1是探头本体的结构示意图；Fig. 1 is the structure diagram of probe body;

图2是淬火介质为水时探头本体内部特征点B3的冷却曲线(图中3表示介质温度为25℃时探头本体内部特征点B3的冷却曲线，4表示介质温度为45℃时探头本体内部特征点B3的冷却曲线，5表示介质温度为60℃时探头本体内部特征点B3的冷却曲线，6表示介质温度为80℃时探头本体内部特征点B3的冷却曲线)；Figure 2 is the cooling curve of the internal feature point B3 of the probe body when the quenching medium is water (3 in the figure indicates the cooling curve of the internal feature point B3 of the probe body when the medium temperature is 25 °C, and 4 indicates the internal characteristics of the probe body when the medium temperature is 45 °C The cooling curve of point B3, 5 indicates the cooling curve of the characteristic point B3 inside the probe body when the medium temperature is 60 °C, and 6 indicates the cooling curve of the characteristic point B3 inside the probe body when the medium temperature is 80 °C);

图3是基于ABAQUS有限元平台建立的探头本体的三维模型；Figure 3 is the three-dimensional model of the probe body established based on the ABAQUS finite element platform;

图4是基于ABAQUS有限元平台建立的探头本体的一维模型；Figure 4 is a one-dimensional model of the probe body established based on the ABAQUS finite element platform;

图5是探头本体在一维模型条件下表面特征点A1和三维模型条件下表面特征点A2的冷却曲线对比图；Fig. 5 is a comparison diagram of the cooling curves of the surface feature point A1 of the probe body under the condition of the one-dimensional model and the surface feature point A2 of the three-dimensional model;

图6是探头本体在一维模型条件内部特征点B1和三维模型条件内部特征点B2的冷却曲线对比图；Fig. 6 is a comparison diagram of the cooling curves of the probe body at the internal feature point B1 of the one-dimensional model condition and the internal feature point B2 of the three-dimensional model condition;

图7是热电偶测得的探头本体内部特征点B3的冷却曲线与探头本体在三维模型条件内部特征点B2的冷却曲线对比图。Fig. 7 is a comparison diagram of the cooling curve of the internal characteristic point B3 of the probe body measured by the thermocouple and the cooling curve of the internal characteristic point B2 of the probe body under the three-dimensional model condition.

具体实施方式 Detailed ways

具体实施方式一：结合图1至图7说明本实施方式，本实施方式的结合有限元法和反传热法计算淬火介质换热系数的方法，所述计算淬火介质换热系数的方法的具体过程为：Specific embodiment 1: This embodiment is described in conjunction with Fig. 1 to Fig. 7, the method of calculating the heat transfer coefficient of quenching medium in this embodiment by combining the finite element method and the reverse heat transfer method, the specific method of calculating the heat transfer coefficient of quenching medium The process is:

步骤一、将内部插有热电偶2的探头本体1在加热炉中加热到860℃保温均匀后，以不超过2s的转移时间迅速淬入淬火介质中，淬火介质温度设定为Tw，采用电脑系统记录由热电偶2测得的探头本体1内部特征点B3的温度，并绘制冷却曲线，即得到此温度下该淬火介质的冷却曲线；Step 1. Heat the probe body 1 with the thermocouple 2 inserted inside to 860°C in the heating furnace and keep it uniform, then quickly quench it into the quenching medium with a transfer time of no more than 2s. The temperature of the quenching medium is set to T w , using The computer system records the temperature of the internal characteristic point B3 of the probe body 1 measured by the thermocouple 2, and draws a cooling curve to obtain the cooling curve of the quenching medium at this temperature;

步骤二、基于ABAQUS有限元平台，采用有限元的方法建立探头本体1的有限元对称模型，输入探头本体1材料的物理性能参数和力学性能参数，设定初始温度850℃，设定淬火介质温度Tw，选取换热系数极大值，选取一维模型的表面特征点A1和内部特征点B1，选取三维模型的表面特征点A2和内部特征点B2，一维模型的表面特征点A1与三维模型的表面特征点A2为同一位置点，一维模型内部特征点B1、三维模型内部特征点B2和探头本体1内部特征点B3为同一点，然后分别采用一维模型和三维模型进行模拟计算并进行比较，探头本体1在一维模型条件下表面特征点A1和三维模型条件下表面特征点A2的冷却曲线重合，探头本体1在一维模型条件内部特征点B1和三维模型条件内部特征点B2的冷却曲线重合，验证换热问题符合的一维性质；Step 2. Based on the ABAQUS finite element platform, use the finite element method to establish a finite element symmetric model of the probe body 1, input the physical and mechanical performance parameters of the probe body 1 material, set the initial temperature to 850°C, and set the temperature of the quenching medium T w , select the maximum heat transfer coefficient, select the surface feature point A1 and internal feature point B1 of the one-dimensional model, select the surface feature point A2 and internal feature point B2 of the three-dimensional model, and select the surface feature point A1 of the one-dimensional model and the three-dimensional feature point The surface feature point A2 of the model is the same position point, the internal feature point B1 of the one-dimensional model, the internal feature point B2 of the three-dimensional model and the internal feature point B3 of the probe body 1 are the same point, and then the one-dimensional model and the three-dimensional model are used for simulation calculation and For comparison, the cooling curves of the surface feature point A1 of the probe body 1 under the condition of the one-dimensional model and the surface feature point A2 under the condition of the three-dimensional model coincide, and the internal feature point B1 of the probe body 1 under the condition of the one-dimensional model and the internal feature point B2 of the three-dimensional model condition The cooling curves coincide to verify that the heat transfer problem conforms to the one-dimensional nature;

步骤三、根据能量守恒定律和傅里叶定律，建立圆柱坐标系下的一维导热微分方程，给出方程的初始条件和边界条件，并且定义与温度具有相同形式的敏感系数方程，给出敏感系数方程的初始条件和边界条件，利用反传热法求解探头本体1表面的热流密度值；Step 3. According to the law of energy conservation and Fourier's law, establish a one-dimensional heat conduction differential equation in the cylindrical coordinate system, give the initial conditions and boundary conditions of the equation, and define the sensitivity coefficient equation with the same form as the temperature, and give the sensitivity The initial conditions and boundary conditions of the coefficient equation, using the inverse heat transfer method to solve the heat flux value on the surface of the probe body 1;

圆柱坐标系下的一维导热微分方程为：The one-dimensional heat conduction differential equation in the cylindrical coordinate system is:

&rho;c&rho;c &PartialD;&PartialD; TT &PartialD;&PartialD; tt == 11 rr &PartialD;&PartialD; &PartialD;&PartialD; rr (( &lambda;r&lambda;r &PartialD;&PartialD; TT &PartialD;&PartialD; rr )) -- -- -- (( 11 ))

式中ρ为密度；c为比热容；T为探头本体表面温度；t为时间；λ为热传导系数；r为探头本体1的半径；In the formula, ρ is the density; c is the specific heat capacity; T is the surface temperature of the probe body; t is the time; λ is the thermal conductivity; r is the radius of the probe body 1;

初始条件为：The initial conditions are:

T(r，tM-1)＝TM-1(r)                                            (2)T(r, t M-1 ) = T M-1 (r) (2)

式中tM-1为M-1时刻；TM-1(r)为tM-1时刻的温度分布；In the formula, t M-1 is the time of M-1; T M-1 (r) is the temperature distribution at the time of t M-1 ;

边界条件为：The boundary conditions are:

-- &lambda;&lambda; &PartialD;&PartialD; TT &PartialD;&PartialD; rr || rr == RR == qq Mm == constconst tt Mm -- 11 << tt << tt Mm qq (( tt )) tt >> tt Mm -- -- -- (( 33 ))

-- &lambda;&lambda; &PartialD;&PartialD; TT &PartialD;&PartialD; rr || rr == 00 == 00 -- -- -- (( 44 ))

式中R为探头本体1的实际半径值；式中tM为M时刻；热流密度qM为常数；q(t)为t时刻的热流密度值；In the formula, R is the actual radius value of the probe body 1; in the formula, t M is the time M; the heat flux q M is a constant; q(t) is the heat flux value at the time t;

定义敏感系数为探头本体1内部点温度测量误差的敏感程度，是温度关于热流密度的一级微商；The sensitivity coefficient is defined as the sensitivity of the temperature measurement error at the internal point of the probe body 1, which is the first-order derivative of the temperature with respect to the heat flux;

敏感系数表达式为：The expression of the sensitivity coefficient is:

&rho;c&rho;c &PartialD;&PartialD; Xx Mm &PartialD;&PartialD; tt == 11 rr &PartialD;&PartialD; &PartialD;&PartialD; rr (( &lambda;r&lambda;r &PartialD;&PartialD; Xx Mm &PartialD;&PartialD; rr )) -- -- -- (( 55 ))

式中XM为敏感系数；Where X M is the sensitivity coefficient;

初始条件为：The initial conditions are:

XM(r，tM-1)＝0                                                  (6)X M (r, t M-1 ) = 0 (6)

式中XM为敏感系数；Where X M is the sensitivity coefficient;

边界条件为：The boundary conditions are:

-- &lambda;&lambda; &PartialD;&PartialD; Xx Mm &PartialD;&PartialD; rr || rr == RR == 11 tt Mm -- 11 << tt << tt Mm 00 tt >> tt Mm -- -- -- (( 77 ))

-- &lambda;&lambda; &PartialD;&PartialD; TT &PartialD;&PartialD; rr || rr == 00 == 00 -- -- -- (( 88 ))

敏感系数对热流密度值进行修正，利用反传热法求解M时刻的热流密度值，反复计算得整个淬火过程的热流密度值q；The sensitivity coefficient corrects the heat flux value, uses the inverse heat transfer method to solve the heat flux value at time M, and repeatedly calculates the heat flux value q of the entire quenching process;

步骤四、根据牛顿换热定律来计算金属与介质表面的换热系数，即得到了介质的换热系数；牛顿换热定律表达式为：Step 4. Calculate the heat transfer coefficient between the metal and the surface of the medium according to Newton's law of heat transfer, that is, the heat transfer coefficient of the medium is obtained; the expression of Newton's law of heat transfer is:

q＝h(T-Tw)                                                (9)q=h(TT w ) (9)

式中q为热流密度值，h为换热系数，(T-Tw)为探头表面温度与设定介质温度的差值；In the formula, q is the heat flux value, h is the heat transfer coefficient, (TT w ) is the difference between the probe surface temperature and the set medium temperature;

本实施方式中将步骤一中热电偶2测得的探头本体1内部特征点B3的温度，并绘制的冷却曲线与步骤二中探头本体1在三维模型条件内部特征点B2的冷却曲线进行对比，两者吻合，验证了换热系数求解的精确性。In this embodiment, the temperature of the internal feature point B3 of the probe body 1 measured by the thermocouple 2 in step 1, and the drawn cooling curve are compared with the cooling curve of the internal feature point B2 of the probe body 1 in the three-dimensional model condition in step 2, The two coincide, which verifies the accuracy of the heat transfer coefficient solution.

具体实施方式二：本实施方式的步骤一中的淬火介质为水、20号机油或UCON-A(水溶性聚合物)淬火剂。Embodiment 2: The quenching medium in the step 1 of this embodiment is water, No. 20 engine oil or UCON-A (water-soluble polymer) quenching agent.

具体实施方式三：本实施方式的步骤一中的淬火介质为水时，淬火介质温度设定为25℃、45℃、60℃或80℃。根据淬火介质物性及实际中的使用温度确定淬火介质的温度，冷却曲线参见图2。Embodiment 3: When the quenching medium in step 1 of this embodiment is water, the temperature of the quenching medium is set to 25°C, 45°C, 60°C or 80°C. Determine the temperature of the quenching medium according to the physical properties of the quenching medium and the actual operating temperature. See Figure 2 for the cooling curve.

具体实施方式四：本实施方式的步骤一中的淬火介质为20号机油时，淬火介质温度设定为25℃、45℃或60℃。根据淬火介质物性及实际中的使用温度确定淬火介质的温度。Embodiment 4: When the quenching medium in step 1 of this embodiment is No. 20 engine oil, the temperature of the quenching medium is set to 25°C, 45°C or 60°C. Determine the temperature of the quenching medium according to the physical properties of the quenching medium and the actual operating temperature.

具体实施方式五：本实施方式的步骤一中的淬火介质为UCON-A(水溶性聚合物)淬火剂时，淬火介质温度设定为25℃、45℃或60℃。根据淬火介质物性及实际中的使用温度确定淬火介质的温度。Embodiment 5: When the quenching medium in step 1 of this embodiment is UCON-A (water-soluble polymer) quenching agent, the temperature of the quenching medium is set to 25°C, 45°C or 60°C. Determine the temperature of the quenching medium according to the physical properties of the quenching medium and the actual operating temperature.

具体实施方式六：本实施方式的步骤一中的探头本体1的线性尺寸为Φ12.5×60mm，探头本体1的材料为镍铬铁基固溶强化合金，热电偶2的直径为1.5mm。Embodiment 6: The linear dimension of the probe body 1 in the step 1 of this embodiment is Φ12.5×60 mm, the material of the probe body 1 is nickel-chromium-iron-based solid-solution strengthened alloy, and the diameter of the thermocouple 2 is 1.5 mm.

具体实施方式七：本实施方式的结合有限元法和反传热法计算淬火介质换热系数的方法，所述计算淬火介质换热系数的方法的具体过程为：Embodiment 7: The method for calculating the heat transfer coefficient of the quenching medium in combination with the finite element method and the reverse heat transfer method of this embodiment, the specific process of the method for calculating the heat transfer coefficient of the quenching medium is as follows:

步骤一、将内部插有热电偶2的探头本体1在加热炉中加热到860℃保温均匀后，以不超过2s的转移时间迅速淬入淬火介质中，淬火介质温度设定为Tw，采用电脑系统记录由热电偶2测得的探头本体1内部特征点B3的温度，并绘制冷却曲线，即得到此温度下该淬火介质的冷却曲线；Step 1. Heat the probe body 1 with the thermocouple 2 inserted inside to 860°C in the heating furnace and keep it uniform, then quickly quench it into the quenching medium with a transfer time of no more than 2s. The temperature of the quenching medium is set to T w , using The computer system records the temperature of the internal characteristic point B3 of the probe body 1 measured by the thermocouple 2, and draws a cooling curve to obtain the cooling curve of the quenching medium at this temperature;

探头本体1的线性尺寸为Φ12.5×60mm，探头本体1的材料为镍铬铁基固溶强化合金(Incone1600)，热电偶2的直径为1.5mm，淬火介质为水，淬火介质温度Tw设定为25℃；冷却曲线参见图2；The linear dimension of the probe body 1 is Φ12.5×60mm, the material of the probe body 1 is nickel-chromium-iron-based solid-solution strengthening alloy (Incone1600), the diameter of the thermocouple 2 is 1.5mm, the quenching medium is water, and the temperature of the quenching medium is Tw Set at 25°C; see Figure 2 for the cooling curve;

步骤二、基于ABAQUS有限元平台，采用有限元的方法建立探头本体1的有限元对称模型，输入探头本体1镍铬铁基固溶强化合金材料的物理性能参数和力学性能参数，设定初始温度850℃，设定淬火介质水的温度Tw为25℃，选取换热系数极大值22000W(m2×K)，选取一维模型的表面特征点A1和内部特征点B1，选取三维模型的表面特征点A2和内部特征点B2，一维模型的表面特征点A1与三维模型的表面特征点A2为同一位置点，一维模型内部特征点B1、三维模型内部特征点B2和探头本体1内部特征点B3为同一点，然后分别采用一维模型和三维模型进行模拟计算并进行比较，探头本体1在一维模型条件下表面特征点A1和三维模型条件下表面特征点A2的冷却曲线重合，探头本体1在一维模型条件内部特征点B1和三维模型条件内部特征点B2的冷却曲线重合，验证换热问题符合的一维性质；参见图3至图6；Step 2. Based on the ABAQUS finite element platform, use the finite element method to establish the finite element symmetric model of the probe body 1, input the physical performance parameters and mechanical performance parameters of the nickel-chromium-iron-based solid-solution strengthening alloy material of the probe body 1, and set the initial temperature 850°C, set the temperature T w of the quenching medium water as 25°C, select the maximum heat transfer coefficient of 22000W (m 2 ×K), select the surface feature point A1 and internal feature point B1 of the one-dimensional model, and select the three-dimensional model Surface feature point A2 and internal feature point B2, the surface feature point A1 of the 1D model and the surface feature point A2 of the 3D model are the same position point, the internal feature point B1 of the 1D model, the internal feature point B2 of the 3D model and the interior of the probe body 1 The feature point B3 is the same point, and then the one-dimensional model and the three-dimensional model are used to perform simulation calculations and comparisons. The cooling curves of the surface feature point A1 of the probe body 1 under the condition of the one-dimensional model and the surface feature point A2 under the condition of the three-dimensional model coincide. The cooling curves of the probe body 1 at the internal feature point B1 under the one-dimensional model condition and the internal feature point B2 under the three-dimensional model condition coincide to verify the one-dimensional nature of the heat transfer problem; see Figures 3 to 6;

步骤三、根据能量守恒定律和傅里叶定律，建立圆柱坐标系下的一维导热微分方程，给出方程的初始条件和边界条件，并且定义与温度具有相同形式的敏感系数方程，给出敏感系数方程的初始条件和边界条件，利用反传热法求解探头本体1表面的热流密度值；Step 3. According to the law of energy conservation and Fourier's law, establish a one-dimensional heat conduction differential equation in the cylindrical coordinate system, give the initial conditions and boundary conditions of the equation, and define the sensitivity coefficient equation with the same form as the temperature, and give the sensitivity The initial conditions and boundary conditions of the coefficient equation, using the inverse heat transfer method to solve the heat flux value on the surface of the probe body 1;

圆柱坐标系下的一维导热微分方程为：The one-dimensional heat conduction differential equation in the cylindrical coordinate system is:

&rho;c&rho;c &PartialD;&PartialD; TT &PartialD;&PartialD; tt == 11 rr &PartialD;&PartialD; &PartialD;&PartialD; rr (( &lambda;r&lambda;r &PartialD;&PartialD; TT &PartialD;&PartialD; rr )) -- -- -- (( 11 ))

式中ρ为密度；c为比热容；T为探头本体表面温度；t为时间；λ为热传导系数；r为探头本体1的半径；In the formula, ρ is the density; c is the specific heat capacity; T is the surface temperature of the probe body; t is the time; λ is the thermal conductivity; r is the radius of the probe body 1;

初始条件为：The initial conditions are:

T(r，tM-1)＝TM-1(r)                                            (2)T(r, t M-1 ) = T M-1 (r) (2)

式中tM-1为M-1时刻；TM-1(r)为tM-1时刻的温度分布；In the formula, t M-1 is the time of M-1; T M-1 (r) is the temperature distribution at the time of t M-1 ;

边界条件为：The boundary conditions are:

-- &lambda;&lambda; &PartialD;&PartialD; TT &PartialD;&PartialD; rr || rr == RR == qq Mm == constconst tt Mm -- 11 << tt << tt Mm qq (( tt )) tt >> tt Mm -- -- -- (( 33 ))

-- &lambda;&lambda; &PartialD;&PartialD; TT &PartialD;&PartialD; rr || rr == 00 == 00 -- -- -- (( 44 ))

式中R为探头本体1的实际半径值；式中tM为M时刻；热流密度qM为常数；q(t)为t时刻的热流密度值；In the formula, R is the actual radius value of the probe body 1; in the formula, t M is the time M; the heat flux q M is a constant; q(t) is the heat flux value at the time t;

定义敏感系数为探头本体1内部点温度测量误差的敏感程度，是温度关于热流密度的一级微商；The sensitivity coefficient is defined as the sensitivity of the temperature measurement error at the internal point of the probe body 1, which is the first-order derivative of the temperature with respect to the heat flux;

敏感系数表达式为：The expression of the sensitivity coefficient is:

&rho;c&rho;c &PartialD;&PartialD; Xx Mm &PartialD;&PartialD; tt == 11 rr &PartialD;&PartialD; &PartialD;&PartialD; rr (( &lambda;r&lambda;r &PartialD;&PartialD; Xx Mm &PartialD;&PartialD; rr )) -- -- -- (( 55 ))

式中XM为敏感系数；Where X M is the sensitivity coefficient;

初始条件为：The initial conditions are:

XM(r，tM-1)＝0                                                    (6)X M (r, t M-1 ) = 0 (6)

式中XM为敏感系数；Where X M is the sensitivity coefficient;

边界条件为：The boundary conditions are:

-- &lambda;&lambda; &PartialD;&PartialD; Xx Mm &PartialD;&PartialD; rr || rr == RR == 11 tt Mm -- 11 << tt << tt Mm 00 tt >> tt Mm -- -- -- (( 77 ))

-- &lambda;&lambda; &PartialD;&PartialD; TT &PartialD;&PartialD; rr || rr == 00 == 00 -- -- -- (( 88 ))

敏感系数对热流密度值进行修正，利用反传热法求解M时刻的热流密度值，反复计算得整个淬火过程的热流密度值q；敏感系数与温度具有相同形式的微分方程，可采用有限差分进行求解热流密度值q；The sensitivity coefficient corrects the heat flux value, uses the inverse heat transfer method to solve the heat flux value at time M, and repeatedly calculates the heat flux value q of the entire quenching process; the sensitivity coefficient and temperature have the same form of differential equation, which can be determined by finite difference Solve for the heat flux value q;

计算起初，假定热流密度值为零，通过敏感系数对热流密度值进行修正，使得修正值足够小；At the beginning of the calculation, it is assumed that the heat flux value is zero, and the heat flux value is corrected by the sensitivity coefficient to make the correction value small enough;

步骤四、根据牛顿换热定律来计算金属与介质表面的换热系数，即得到了介质的换热系数；牛顿换热定律表达式为：Step 4. Calculate the heat transfer coefficient between the metal and the surface of the medium according to Newton's law of heat transfer, that is, the heat transfer coefficient of the medium is obtained; the expression of Newton's law of heat transfer is:

q＝h(T-Tw)                                                       (9)q=h(TT w ) (9)

式中q为热流密度值，h为换热系数，(T-Tw)为探头表面温度与设定介质温度的差值；In the formula, q is the heat flux value, h is the heat transfer coefficient, (TT w ) is the difference between the probe surface temperature and the set medium temperature;

本实施方式中将步骤一中热电偶2测得的探头本体1内部特征点B3的温度，并绘制的冷却曲线与步骤二中探头本体1在三维模型条件内部特征点B2的冷却曲线进行对比，两者吻合，验证了换热系数求解的精确性。In this embodiment, the temperature of the internal feature point B3 of the probe body 1 measured by the thermocouple 2 in step 1, and the drawn cooling curve are compared with the cooling curve of the internal feature point B2 of the probe body 1 in the three-dimensional model condition in step 2, The two coincide, which verifies the accuracy of the heat transfer coefficient solution.

Claims (7)

1. in conjunction with a method for finite element method and the inverse heat conduction method calculating hardening media coefficient of heat transfer, it is characterized in that: the detailed process of the method for the described calculating hardening media coefficient of heat transfer is:
Step 1, the probe body (1) that inside is inserted with to thermopair (2) are heated to after 860 ℃ of insulations evenly in heating furnace, to be no more than the transfer time of 2s, quench rapidly in hardening media, and quench media temperature is set as T w, adopt computer system to record the temperature of probe body (1) the inter characteristic points B3 being recorded by thermopair (2), and draw cooling curve, obtain the cooling curve of this hardening media at this temperature;
Step 2, based on ABAQUS finite element platform, adopt the finite element symmetry model of the method foundation probe body (1) of finite element, physical function parameter and the mechanical property parameters of input probe body (1) material, set 850 ℃ of initial temperatures, sets quench media temperature T w, choose coefficient of heat transfer maximum value, choose surface characteristics point A1 and the inter characteristic points B1 of one-dimensional model, choose surface characteristics point A2 and the inter characteristic points B2 of three-dimensional model, the surface characteristics point A1 of one-dimensional model and the surface characteristics point A2 of three-dimensional model are same position point, one-dimensional model inter characteristic points B1, three-dimensional model inter characteristic points B2 and probe body (1) inter characteristic points B3 are same point, then adopt respectively one-dimensional model and three-dimensional model carry out analog computation and compare, probe body (1) overlaps at the cooling curve of one-dimensional model condition lower surface unique point A1 and three-dimensional model condition lower surface unique point A2, probe body (1) overlaps at the cooling curve of one-dimensional model condition inter characteristic points B1 and three-dimensional model condition inter characteristic points B2, the one dimension character that checking heat transfer problem meets,
Step 3, according to law of conservation of energy and Fourier law, set up the one-dimensional heat conduction differential equation under cylindrical-coordinate system, provide starting condition and the boundary condition of equation, and definition and temperature field have the sensitivity coefficient equation of same form, provide starting condition and the boundary condition of sensitivity coefficient equation, utilize inverse heat conduction method to solve the heat flow density value on probe body (1) surface;
The one-dimensional heat conduction differential equation under cylindrical-coordinate system is:
&rho;c &PartialD; T &PartialD; t = 1 r &PartialD; &PartialD; r ( &lambda;r &PartialD; T &PartialD; r ) - - - ( 1 )
In formula, ρ is density; C is specific heat capacity; T is probe body surface temperature; T is the time; λ is heat-conduction coefficient; r
Radius for probe body (1);
Starting condition is:
T(r,t M-1)=T M-1(r) (2)
T in formula m-1for the M-1 moment; T m-1(r) be t m-1temperature Distribution constantly;
Boundary condition is:
- &lambda; &PartialD; T &PartialD; r | r = R = q M = const t M - 1 < t < t M q ( t ) t > t M - - - ( 3 )
- &lambda; &PartialD; T &PartialD; r | r = 0 = 0 - - - ( 4 )
In formula, R is the real radius value of probe body (1); T in formula mfor the M moment; Heat flow density q mfor constant; Q (t) is t heat flow density value constantly;
Definition sensitivity coefficient, for the sensitivity of probe body (1) internal point thermometric error, is that temperature is about the first derivative of heat flow density;
Sensitivity coefficient expression formula is:
&rho;c &PartialD; X M &PartialD; t = 1 r &PartialD; &PartialD; r ( &lambda;r &PartialD; X M &PartialD; r ) - - - ( 5 )
X in formula mfor sensitivity coefficient;
Starting condition is:
X M(r,t M-1)=0 (6)
X in formula mfor sensitivity coefficient;
Boundary condition is:
- &lambda; &PartialD; X M &PartialD; r | r = R = 1 t M - 1 < t < t M 0 t > t M - - - ( 7 )
- &lambda; &PartialD; T &PartialD; r | r = 0 = 0 - - - ( 8 )
Sensitivity coefficient is revised heat flow density value, utilizes inverse heat conduction method to solve M heat flow density value constantly, repeatedly calculates the heat flow density value q of whole quenching process;
Step 4, according to newton's heat exchange law, calculate the coefficient of heat transfer of metal and dielectric surface, obtained the coefficient of heat transfer of medium; Newton's heat exchange law expression formula is:
q=h(T-T w) (9)
In formula, q is heat flow density value, and h is the coefficient of heat transfer, (T-T w) be surface temperature of probe and the difference of setting medium temperature.
2. combination finite element method according to claim 1 and inverse heat conduction method calculate the method for the hardening media coefficient of heat transfer, it is characterized in that: the hardening media in step 1 is water, No. 20 machine oil or UCON-A quenching medium.
3. combination finite element method according to claim 2 and inverse heat conduction method calculate the method for the hardening media coefficient of heat transfer, it is characterized in that: when the hardening media in step 1 is water, quench media temperature is set as 25 ℃, 45 ℃, 60 ℃ or 80 ℃.
4. combination finite element method according to claim 2 and inverse heat conduction method calculate the method for the hardening media coefficient of heat transfer, it is characterized in that: when the hardening media in step 1 is No. 20 machine oil, quench media temperature is set as 25 ℃, 45 ℃ or 60 ℃.
5. combination finite element method according to claim 2 and inverse heat conduction method calculate the method for the hardening media coefficient of heat transfer, it is characterized in that: when the hardening media in step 1 is UCON-A quenching medium, quench media temperature is set as 25 ℃, 45 ℃ or 60 ℃.
6. combination finite element method according to claim 1 and inverse heat conduction method calculate the method for the hardening media coefficient of heat transfer, it is characterized in that: the linear dimension of the probe body (1) in step 1 is Φ 12.5 * 60mm, the material of probe body (1) is nickel chromium triangle iron-based solid solution strengthened alloy, and the diameter of thermopair (2) is 1.5mm.
7. in conjunction with a method for finite element method and the inverse heat conduction method calculating hardening media coefficient of heat transfer, it is characterized in that: the detailed process of the method for the described calculating hardening media coefficient of heat transfer is:
Step 1, the probe body (1) that inside is inserted with to thermopair (2) are heated to after 860 ℃ of insulations evenly in heating furnace, to be no more than the transfer time of 2s, quench rapidly in hardening media, and quench media temperature is set as T w, adopt computer system to record the temperature of probe body (1) the inter characteristic points B3 being recorded by thermopair (2), and draw cooling curve, obtain the cooling curve of this hardening media at this temperature;
The linear dimension of probe body (1) is Φ 12.5 * 60mm, and the material of probe body (1) is nickel chromium triangle iron-based solid solution strengthened alloy, and the diameter of thermopair (2) is 1.5mm, and hardening media is water, quench media temperature T wbe set as 25 ℃;
Step 2, based on ABAQUS finite element platform, adopt the finite element symmetry model of the method foundation probe body (1) of finite element, physical function parameter and the mechanical property parameters of input probe body (1) nickel chromium triangle iron-based solid solution strengthened alloy material, set 850 ℃ of initial temperatures, set the temperature T of hardening media water wbe 25 ℃, choose coefficient of heat transfer maximum value 22000W (m 2* K), choose surface characteristics point A1 and the inter characteristic points B1 of one-dimensional model, choose surface characteristics point A2 and the inter characteristic points B2 of three-dimensional model, the surface characteristics point A1 of one-dimensional model and the surface characteristics point A2 of three-dimensional model are same position point, one-dimensional model inter characteristic points B1, three-dimensional model inter characteristic points B2 and probe body (1) inter characteristic points B3 are same point, then adopt respectively one-dimensional model and three-dimensional model carry out analog computation and compare, probe body (1) overlaps at the cooling curve of one-dimensional model condition lower surface unique point A1 and three-dimensional model condition lower surface unique point A2, probe body (1) overlaps at the cooling curve of one-dimensional model condition inter characteristic points B1 and three-dimensional model condition inter characteristic points B2, the one dimension character that checking heat transfer problem meets,
Step 3, according to law of conservation of energy and Fourier law, set up the one-dimensional heat conduction differential equation under cylindrical-coordinate system, provide starting condition and the boundary condition of equation, and definition and temperature field have the sensitivity coefficient equation of same form, provide starting condition and the boundary condition of sensitivity coefficient equation, utilize inverse heat conduction method to solve the heat flow density value on probe body (1) surface;
The one-dimensional heat conduction differential equation under cylindrical-coordinate system is:
&rho;c &PartialD; T &PartialD; t = 1 r &PartialD; &PartialD; r ( &lambda;r &PartialD; T &PartialD; r ) - - - ( 1 )
In formula, ρ is density; C is specific heat capacity; T is probe body surface temperature; T is the time; λ is heat-conduction coefficient; r
Radius for probe body (1);
Starting condition is:
T(r,t M-1)=T M-1(r) (2)
T in formula m-1for the M-1 moment; T m-1(r) be t m-1temperature Distribution constantly;
Boundary condition is:
- &lambda; &PartialD; T &PartialD; r | r = R = q M = const t M - 1 < t < t M q ( t ) t > t M - - - ( 3 )
- &lambda; &PartialD; T &PartialD; r | r = 0 = 0 - - - ( 4 )
In formula, R is the real radius value of probe body (1); T in formula mfor the M moment; Heat flow density q mfor constant; Q (t) is t heat flow density value constantly;
Definition sensitivity coefficient, for the sensitivity of probe body (1) internal point thermometric error, is that temperature is about the first derivative of heat flow density;
Sensitivity coefficient expression formula is:
&rho;c &PartialD; X M &PartialD; t = 1 r &PartialD; &PartialD; r ( &lambda;r &PartialD; X M &PartialD; r ) - - - ( 5 )
X in formula mfor sensitivity coefficient;
Starting condition is:
X M(r,t M-1)=0 (6)
X in formula mfor sensitivity coefficient;
Boundary condition is:
- &lambda; &PartialD; X M &PartialD; r | r = R = 1 t M - 1 < t < t M 0 t > t M - - - ( 7 )
- &lambda; &PartialD; T &PartialD; r | r = 0 = 0 - - - ( 8 )
Sensitivity coefficient is revised heat flow density value, utilizes inverse heat conduction method to solve M heat flow density value constantly, repeatedly calculates the heat flow density value q of whole quenching process;
Step 4, according to newton's heat exchange law, calculate the coefficient of heat transfer of metal and dielectric surface, obtained the coefficient of heat transfer of medium; Newton's heat exchange law expression formula is:
q=h(T-T w) (9)
In formula, q is heat flow density value, and h is the coefficient of heat transfer, (T-T w) be surface temperature of probe and the difference of setting medium temperature.
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